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Avtomat. i Telemekh., 2015, Issue 6, Pages 42–56 (Mi at14243)  

This article is cited in 10 scientific papers (total in 10 papers)

Nonlinear Systems

On existence conditions for a two-point oscillating periodic solution in an non-autonomous relay system with a Hurwitz matrix

V. V. Yevstafyeva

St. Petersburg State University, St. Petersburg, Russia

Abstract: We consider a system of differential equations with relay nonlinearity and an external continuous periodic influence. For system parameters, we obtain sufficient existence and uniqueness conditions for a two-point oscillating solution with given period in case of a Hurwitz system matrix. With exact analytic approaches, we find time moments and switching points in the phase space of the image point for a solution whose period is a multiple of the period of external disturbances. We obtain conditions on system parameters for which a solution in the considered class is asymptotically-orbital stable.

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English version:
Automation and Remote Control, 2015, 76:6, 977–988

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Presented by the member of Editorial Board: А. М. Красносельский

Received: 10.05.2013

Citation: V. V. Yevstafyeva, “On existence conditions for a two-point oscillating periodic solution in an non-autonomous relay system with a Hurwitz matrix”, Avtomat. i Telemekh., 2015, no. 6, 42–56; Autom. Remote Control, 76:6 (2015), 977–988

Citation in format AMSBIB
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\paper On existence conditions for a~two-point oscillating periodic solution in an non-autonomous relay system with a~Hurwitz matrix
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\yr 2015
\issue 6
\pages 42--56
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\transl
\jour Autom. Remote Control
\yr 2015
\vol 76
\issue 6
\pages 977--988
\crossref{https://doi.org/10.1134/S000511791506003X}
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. A. M. Kamachkin, G. M. Chitrov, V. N. Shamberov, “Algebraical aspects of parametrical decomposition method”, 2015 International Conference “Stability and Control Processes” in Memory of V.I. Zubov (SCP), eds. L. Petrosyan, A. Zhabko, IEEE, 2015, 52–54  isi
    2. V. N. Starkov, N. A. Stepenko, “Simulation of particle motion in the given speed fields”, 2015 International Conference “Stability and Control Processes” in Memory of V.I. Zubov (SCP), eds. L. Petrosyan, A. Zhabko, IEEE, 2015, 75–77  isi
    3. A. M. Kamachkin, D. K. Potapov, V. V. Yevstafyeva, “Non-existence of periodic solutions to non-autonomous second-order differential equation with discontinuous nonlinearity”, Electron. J. Differ. Equ., 2016, 04  mathscinet  zmath  isi
    4. A. M. Kamachkin, D. K. Potapov, V. V. Yevstafyeva, “Existence of periodic solutions to automatic control system with relay nonlinearity and sinusoidal external influence”, Int. J. Robust Nonlinear Control, 27:2 (2017), 204–211  crossref  mathscinet  zmath  isi  elib  scopus
    5. A. M. Kamachkin, G. M. Khitrov, V. N. Shamberov, “Normalnye formy matrits v zadachakh dekompozitsii i upravleniya mnogomernykh sistem”, Vestn. S.-Peterburg. un-ta. Ser. 10. Prikl. matem. Inform. Prots. upr., 13:4 (2017), 417–430  mathnet  crossref  elib
    6. A. M. Kamachkin, D. K. Potapov, V. V. Yevstafyeva, “Existence of subharmonic solutions to a hysteresis system with sinusoidal external influence”, Electron. J. Differ. Equ., 2017, 140  mathscinet  zmath  isi
    7. A. M. Kamachkin, D. K. Potapov, V. V. Yevstafyeva, “On uniqueness and properties of periodic solution of second-order nonautonomous system with discontinuous nonlinearity”, J. Dyn. Control Syst., 23:4 (2017), 825–837  crossref  mathscinet  zmath  isi  scopus
    8. A. M. Kamachkin, V. N. Shamberov, G. M. Chitrov, “Special matrix transformations of essential nonlinear control systems”, Constructive Nonsmooth Analysis and Related Topics, CNSA 2017, Dedicated to the Memory of V. F. Demyanov, ed. L. Polyakova, IEEE, 2017, 138–140  isi
    9. Yevstafyeva V.V., “Periodic Solutions of a System of Differential Equations With Hysteresis Nonlinearity in the Presence of Eigenvalue Zero”, Ukr. Math. J., 70:8 (2019), 1252–1263  crossref  mathscinet  isi
    10. A. M. Kamachkin, D. K. Potapov, V. V. Evstafeva, “Dinamika i sinkhronizatsiya tsiklicheskikh struktur ostsillyatorov s gisterezisnoi obratnoi svyazyu”, Vestn. S.-Peterburg. un-ta. Ser. 10. Prikl. matem. Inform. Prots. upr., 16:2 (2020), 186–199  mathnet  crossref
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